In the applied sciences, various fields of study require the analysis of two-dimensional or three-dimensional volume data-sets wherein each data-set may have multiple attributes representing different physical properties. An attribute, sometimes referred to as a data value, represents a particular physical property of an object within a defined two-dimensional or three-dimensional space. A data value may, for instance, be an 8-byte data word which includes 256 possible values. The location of an attribute is represented by (x, y, data value) or (x, y, z, data value). If the attribute represents pressure at a particular location, then the attribute location may be expressed as (x, y, z, pressure).
In the medical field, a computerized axial topography (CAT) scanner or magnetic resonance imaging (MRI) device is used to produce a picture or diagnostic image of some specific area of a person's body, typically representing the coordinate and a determined attribute. Normally, each attribute within a predetermined location must be imaged separate and apart from another attribute. For example, one attribute representing temperature at a predetermined location is typically imaged separate from another attribute representing pressure at the same location. Thus, the diagnosis of a particular condition based upon these attributes is limited by the ability to display a single attribute at a predetermined location.
In the field of earth sciences, seismic sounding is used for exploring the subterranean geology of an earth formation. An underground explosion excites seismic waves, similar to low-frequency sound waves that travel below the surface of the earth and are detected by seismographs. The seismographs record the amplitude of seismic waves, both direct and reflected, at a given location for a given time period. Knowing the time and place of the explosion, the time of travel of the waves through the interior can be calculated and used to measure the velocity of the waves in the interior. A similar technique can be used for offshore oil and gas exploration. In offshore exploration, a ship tows a sound source and underwater hydrophones. Low frequency, (e.g., 50 Hz) sound waves are generated by, for example, a pneumatic device that works like a balloon burst. The sounds bounce off rock layers below the sea floor and are picked up by the hydrophones. In either application, subsurface sedimentary structures that trap oil, such as faults and domes are mapped by the reflective waves.
The use of seismic data to analyze subsurface geological structures, such as faults or other stratographic features, is relevant to interpreters searching for subsurface mineral and hydrocarbon deposits. Seismic-data traces are the record of the reflection of sonic waves from underground. These traces can be denoted as A(x, y, t), the reflection amplitude of time t at surface location (x, y). A wiggle display is a basic graphic representation for seismic applications, which may be displayed as a two-dimensional or a three-dimensional image. The area of the amplitude above and/or below a given reference amplitude value for a given wiggle can be filled with colors to enhance the wiggle display for interpretation purposes and therefore, make faults and other stratigraphic features revealed by the wiggle display easier to recognize as generally described in U.S. Pat. No. 7,013,218, which is incorporated herein by reference.
The seismic data is collected and processed to produce three-dimensional volume data-sets comprising “voxels” or volume elements, whereby each voxel may be identified by the x, y, z coordinates of one of its eight corners or its center. Each voxel also represents a numeric data value (attribute) associated with some measured or calculated physical property at a particular location. Examples of geological seismic data values include amplitude, phase, frequency, and semblance. Different data values are stored in different three-dimensional volume data-sets, wherein each three-dimensional volume data-set represents a different data value. When multitude data-sets are used, the data value for each of the data-sets may represent a different physical parameter or attribute for the same geographic space. By way of example, a plurality of data-sets could include a seismic volume, a temperature volume and a water-saturation volume. The voxels in the seismic volume can be expressed in the form (x, y, z, seismic amplitude). The voxels in the temperature volume can be expressed in the form (x, y, z, ° C.). The voxels in the water-saturation volume can be expressed in the form (x, y, z, % saturation). The physical or geographic space defined by the voxels in each of these volumes is the same. However, for any specific spatial location (xo, yo, zo), the seismic amplitude would be contained in the seismic volume, the temperature in the temperature volume and the water-saturation in the water-saturation volume. In order to analyze certain sub-surface geological structures, sometimes referred to as “features” or “events,” information from different three-dimensional volume data-sets may be separately imaged in order to analyze the feature or event.
The relationship between a typical wiggle or seismic-data trace and a plurality of voxels is described more fully in U.S. Pat. No. 6,690,820 assigned to Landmark Graphics Corporation, which is incorporated herein by reference.
The presence of geologic structure typically distorts the view of stratigraphic detail in the conventional variable area and/or wiggle trace displays of seismic data often used to interpret subsurface geology. Because the trace is vertical, it does not intersect a horizon at right angles, which is the direction of maximum resolution.
Geological interpreters often use palinspastic reconstruction to, at least approximately, reverse geologic time and warp their modern day structural model into a model of the geologic structure as it would have appeared at some past time. Seismic interpreters will sometimes use a seismic paleosection on which some selected horizon is flattened in order to approximately reveal the attitude of deeper structure at the time of deposition of the flattened horizon. In either approach, however, compaction due to overburden and other changes subsequent to deposition are often ignored.
In 1982, a technique known as downward continuation or wave-equation datuming was adapted for horizon flattening in the Society of Exploration Geophysicists Technical Program Expanded Abstracts S8.7 under the title Paleo Seismic and Color Acoustic Impedance Sections Applications of Downward Continuation in Structural and Stratigraphic Context by M. Turhan Taner, Ernest E. Cook and Norman S. Neidell. This technique was applied to a stacked seismic section for a more sophisticated, and presumably more accurate, way to generate paleosections than just arbitrarily shifting each individual trace up or down to flatten a selected horizon. This technique was later extended to prestack seismic data in the article Prestack Layer Replacement by Oz Yilmaz and Darren Lucas published in Geophysics, Vol. 51, No. 7.
The wave-equation technique, designated as an aid to structural interpreters, also removed waveform distortions due to overburden structure and reflector orientation for the particular target horizon being flattened. The wave-equation technique further recognized that the process could be reiterated by selecting a deeper horizon and redatuming to it from the previously flattened horizon. While the application was to two-dimensional unmigrated seismic data back in that era, that technique can also, in principle, be applied to modern day unmigrated three dimensional data as well. The computational cost of 3D wave equation redatuming is fairly large, however, making it quite unsuitable in general to interactive seismic interpretation when more than a small handful of seismic horizons are of interest. In addition, the need for unmigrated stacked data, while quite common back in 1982, imposes an unnatural requirement in the modern era where interpreters are very often provided time-migrated volumes as their fundamental input data. However attractive wave equation redatuming might be for unravelling the effects of present-day complex overburden and structure, there is a need for methods and processes that are far less computationally intensive and only require a time-migrated input dataset.
In 1998, an article in Geophysics (volume 63, page 743) entitled Resolution in Seismic Imaging: Is it all a Matter of Perspective? by Stewart A. Levin rigorously examined the general scientific community perception that, unlike wave equation redatuming, migration inherently distorted and degraded waveforms for all but the simplest horizontal subsurface geometries. Rejecting then conventional wisdom, the author argued that, among other things, stratigraphic resolution in two-dimensional migrated sections is not inherently distorted by subsurface structure, but instead is generally only an artifact of the universal choice of vertical trace display. Indeed, a horizontal trace display reversed the apparent roles of low and high frequency waveform appearance. It is this insight into the true relationship between iterated wave equation redatuming and seismic time migration that is the launching point for the present invention in addressing the need for interactive interpretation of structurally complex migrated images without distortion and degradation of seismic resolution.